Vortex domain structures of an epitaxial ferroelectric nanodot and its temperature-misfit strain phase diagram

Phase field simulations were conducted to investigate the effect of misfit strain on the vortex domain structure (VDS) in a BaTiO3 nanodot. Taking into account the effect of inhomogeneous eletromechanical fields, ambient temperature and surface effects, our calculations demonstrate a strong effect of misfit strain on the orientation and magnitude of the polarization dipoles. As a consequence, fruitful equilibrium vortex domain patterns can be obtained by adjusting the epitaxial misfit strain between the substrate and the nanodot. While the nanodot exhibits a single transition from a paraelectric to a near-rhombohedral vortex state at zero misfit strain with the decrease of temperature, complicated transformations of vortex domain patterns are found under nonzero misfit strain. Typically, orthorhombic, tetragonal and several unreported vortex domain patterns (e. g., with zero toroidal moment) are found. Moreover, misfit strain-induced transformations into these domain patterns are also predicted for a ferroelectric nanodot with initial near-rhombohedral vortex state. Combining effects of the ambient temperature and misfit strain, a "temperature-misfit strain" phase-diagram depicting the fruitful vortex domain patterns of the nanodot was obtained. Our simulations indicate promising application of strain engineering in controlling the VDS in ferroelectric nanostructures.